Bowling
The Tigers have had some sports over the years that they elected to discontinue, most notably swimming and wrestling. Cost-cutting was most likely the biggest reason, but there is also one contrast between those sports against the newest ones that Clemson has recently added.
Softball and Gymnastics have become big hits with Tiger fans because they are genuine spectator sports. Lacrosse is opening a new facility this year and they are beginning to gain steam with the fanbase too.
There are several NCAA options for adding sports, such as:
Rifle: this does seem a reasonably natural fit for a university in an area where hunting is prevalent, but it isn’t much for spectators.
Fencing: Fencing is neat but I don’t often gravitate towards it when it's in the Olympics, so not sure many would at the college level.
Beach Volleyball: this is an option. You don’t have to be near the beach. Ohio State, Penn State, TCU, and Loyola Chicago all have women’s teams, men’s teams, or both.
Water Polo: All you need is a pool, but it does seem to be limited to West Coast schools and the Ivy League.
Field Hockey: another sound option.
In the end, though, I think there is an option that would be a sneaky good add as a varsity sport: bowling.
If you are from my era at Clemson, you remember the bowling alley in the Student Union. For on-campus students, it was a nice recreation option.
If Clemson were to create a nice facility for students and spectators that could serve as a place for the team to compete but could also be open to students when the team isn’t playing or practicing, I think that would be a big hit.